To begin with, a political machine is an organization in which an organization gains support via promising rewards to those who keep them in power. It's designed to keep a particular group in power by promising favors. Typically, immigrants who first arrived here were impoverished, so political machines became so successful because they would promise to set immigrants up with homes or jobs or food so long as they had their vote.
So in short:
Who: Organizations whose main goals were getting and keeping power.
What: They essentially bribed immigrants for their votes.
Why: Political Machines did this to stay in power.